Just about all familiar materials (e.g. glass or water) have positive values for both electric permittivity (∈) and magnetic permeability (μ). It is less well recognized that materials are common for which ∈ is negative. Many metals (e.g., gold and silver) have negative ∈ at wavelengths in the visible spectrum. A material having either (but not both) ∈ or μ less than zero is opaque to electromagnetic radiation.
While material response is fully characterized by the parameters ∈ and μ, the optical properties of a transparent material are often more conveniently described by a different parameter, the index of refractive, n, given by n=√{square root over (∈μ)}. Typically, the index of refraction n determines the factor to which the propagation of light in a medium is slower than in a vacuum.
Most of the time, n is larger than unity. A wave travels more slowly in a medium such as glass or water by the factor n.
Under conditions of negative refraction, a light wave impinging from vacuum or air onto the material's surface under an angle with respect to the surface normal is refracted toward the “wrong” side of the normal. A negative index of refraction, n, in Snell's law indeed reproduces this unusual behavior. Mathematically, the square of the index of refraction, n2=∈μ. If both permittivity and permeability are negative, the resulting refractive index is negative as well. A negative permittivity is not unusual and occurs in any metal from zero frequency to the plasma frequency; however, a large magnetic response, in general, and a negative permeability at optical frequencies, in particular, do not occur in natural materials.
Negative refraction is currently achieved by a combination of artificial “electric atoms” (metallic wires with negative electrical permittivity ∈) and artificial “magnetic atoms” (split-ring resonators with negative magnetic permeability μ). Both ∈ and μ must be negative at the same frequency, which is not easy to be achieved at higher than THz frequencies. All negative refraction index material (NIM) implementations to date have utilized the topology consisting of split-ring resonators (SRRs) (rings with gaps, providing the negative μ) and continuous wires (providing the negative ∈). NIMs with an index of refraction n=−1 have been fabricated with losses of less than 1 dB/cm. It has recently been observed indirectly NIMs having negative μ at the THz region. However, in most of the THz experiments, only one layer of SRRs were fabricated on a substrate and the transmission, T, was measured only for propagation perpendicular to the plane of the SRRs, exploiting the coupling of the electric field to the magnetic resonance of the SRR via asymmetry. This way it is not possible to drive the magnetic permeability negative. Also, no negative n has been directly observed yet at the THz region. One reason is that is very difficult to measure with the existing topology of SRRs and continuous wires both the transmission, T, and reflection, R, along the direction parallel to the plane of the SRRs.